Weakly-coupled trace anomaly action for gravity

In this paper, we discuss a local, diff-invariant quantum effective action for gravity that captures the trace anomaly via a counter-term. We discuss why this counter-term is the most significant among infinitely many possible ones, and show how the counter-term leads to a scattering amplitude that is strongly coupled at arbitrarily low energies. We show how the introduction of a new sector with spontaneously broken scale invariance removes the strong coupling problem, and discuss some physical consequences due to the new sector. Three Appendices summarize quantum effective actions — highlighting connections between their local, and seemingly nonlocal formulations — for the scale anomaly in 4D QED, for the axial anomaly in 2D QED, and for the scale anomaly in a 2D sigma model.